# Full text of "Mathematical And Physical Papers - Iii"

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ON THE MOTION OF PENDULUMS.
Ill
have much the same effect as a rigid plane, inasmuch as it would be preserved almost exactly horizontal by the action of gravity. The vessel which contained the water was 51 inches long and 17 broad, the water was 14 inches deep, and the spheres were plunged to about 8 inches below the surface, so that the effect of the confinement of the fluid mass would have been quite sensible in the case of such large spheres. If it be objected that the same sphere gave negative differences in the case of the first group of experiments, it must be observed, that when the apparent weight of so large a sphere was only 2102 French grains, the resistance would quickly have caused the oscillations to subside if an extraneous force had not frequently been applied.
71. In Dubuat's experiments on spheres oscillating in air, the lightness of the fluid was compensated by the extreme lightness of the spheres, which were composed, the first two of paper, and the third of goldbeater's skin. In the following table the diameter 2a of the sphere is expressed in French inches. The value of vV6' employed in the reduction is the same as was before used in the reduction of observations made in air, namely 0*116 inch English, or 01088 inch French.
Dubuat's experiments on light spheres oscillating in
air.
No.	2a	T	n calc.	n obs.	Bid'.
337	4-0416	1-51	1-61	1-51	-o-io
338	6'625	1-84	1-57	1-63	-f-O-Ofj
339	17-25	3-625	1-53	1-54	+0-0:1.
The differences certainly appear very small when the delicacy of the experiments and the simplicity of the apparatus employed are considered.
72. The only comparison yet made in this section between theory and observation in the case of pendulum experiments, consists in comparing the observed times of vibration with the results calculated with an assumed value of *Jp!. But according to theory we ought to be able, without assigning a particular value to any new disposable constant, to calculate the rate of decrease of the arc of vibration, I have not met with any experiments
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